The budget drew stinging criticism from the EU's top economic affairs officials, who penned a letter to Rome describing its plans as "unprecedented" and warning that Brussels does not rule out rejecting the entire budget.
Ahead of the meeting, Italy had on Wednesday insisted it would not budge on the budget, putting Rome squarely on course for a clash with Brussels.
Italy has until Monday to explain to the commission its breach of rules and faces the rejection of its budget, which could eventually lead to sanctions.
The Italian government has until midday Monday to respond to the European Union letter, which expresses concern about Italy's structural deficit and its high debt level, and seeks more information about Italy's growth outlook from its new populist government.
"I cannot imagine the euro without Italy and Italy without the euro, " Moscovici said after his meeting with Tria during which he delivered the letter.
"The economic plans of the government, while supportive of growth in the near term, do not amount to a coherent programme of reforms that will lift Italy's mediocre growth performance on a sustained basis", it said. The agency rates Italy's debt "BBB" with a stable outlook, following an upgrade from "BBB-" last October.
Despite the strong language in a letter deeming the budget inadmissible, both the Italian premier and economic minister continued to voice optimism that they could win consent by illustrating their plans.
The head of one of Italy's two ruling parties says the government won't fall over a dispute on the budget draft, which would offer a tax amnesty to Italians with accounts overseas.
Nevertheless, an Italian government source told dpa that a negative European Union verdict would likely come on Tuesday, when the EuropeanÂ Commission is due to hold its weekly meeting in Strasbourg.
At the summit, Austrian Chancellor Sebastian Kurz said fiscal rules should be respected by all, adding: "Too much debt is risky".
The EU commission chief said Italy have used all the elements of flexibility of EU rules, and that leaders don't want to add more room for manoeuvre for Italy.
Luigi Di Maio, the head of the 5-Star Movement, said Friday that he was sure a solution would be found, adding "we will hardly let the government fall over an amnesty for whoever launders or self-launders money".
The populist government, made up of the 5-Star Movement and Salvini's League, planned an emergency Cabinet meeting later Saturday to discuss the budget and claims by the 5-Star leader that unauthorized changes were made to the draft budget.
Rutte said in a statement that he expressed Dutch concerns regarding Italy's budget plans and said he was giving "full support" to the European Commission, which is vetting the draft after having expressed its skepticism.